Extremum statistics in scale-free network models.

We investigate the statistics of the most connected node in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation, due to the finite size of the network, of the degree distribution governs the scaling of the extreme values and that the distribution of maxima follows the Gumbel statistics. For a scale-free network model with heterogeneous nodes, we show that scaling no longer holds and that the truncation of the degree distribution no longer controls the maxima distribution.